The Engineering Project Organizational Journal (Vol. 3, 2013) published the results of an exploratory study designed to gain a better understanding of how the emotional intelligence of individual team members relates directly to the performance of their team during an engineering project. Undergraduate students enrolled in the course Introduction to the Building Industry participated in the study. All students completed an emotional intelligence test and received an interpersonal score, stress management score, and mood score. Students were grouped into n = 23 teams and assigned a group project. However, each student received an individual project score. These scores were averaged to obtain the dependent variable in the analysis: mean project score (y). Three independent variables were determined for each team: range of interpersonal scores (x1), range of stress management scores (x2), and range of mood scores (x3). Data (simulated from information provided in the article) are listed in the table.

a. Hypothesize a first-order model for project score (y) as a function of x1, x2, and x3.
b. Fit the model, part a, to the data using statistical software.
c. Is there sufficient evidence to indicate the overall model is statistically useful for predicting y? Test using α =| .05.
d. Evaluate the model statistics R2α and 2s.
e. Find and interpret a 95% prediction interval for y when x1 = 20, x2 = 30, and x3 = 25.

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Intrapersonal (Range) Stress Mood Project (Average) Team (Range) (Range) 17 88.0 86.0 83.5 85.5 90.0 90.5 94.0 85.5 88.0 91.0 91.5 91.5 86.0 83.0 85.0 84.0 85.5 85.0 84.5 83.5 85.0 92.5 89.0 2 21 26 6. 4. 5 28 27 21 20 8. 16 17 18 10 11 12 13 14 15 16 17 18 19 20 21 22 23 10 28 19 26 11 27 16 20 10 17